networkx.algorithms.bipartite.projection.generic_weighted_projected_graph¶

generic_weighted_projected_graph(B, nodes, weight_function=None)[source]¶

Weighted projection of B with a user-specified weight function.

The bipartite network B is projected on to the specified nodes with weights computed by a user-specified function. This function must accept as a parameter the neighborhood sets of two nodes and return an integer or a float.

The nodes retain their attributes and are connected in the resulting graph if they have an edge to a common node in the original graph.

Parameters

B (NetworkX graph) – The input graph should be bipartite.
nodes (list or iterable) – Nodes to project onto (the “bottom” nodes).
weight_function (function) – This function must accept as parameters the same input graph that this function, and two nodes; and return an integer or a float. The default function computes the number of shared neighbors.

Returns

Graph – A graph that is the projection onto the given nodes.

Return type

NetworkX graph

Examples

>>> from networkx.algorithms import bipartite
>>> # Define some custom weight functions
>>> def jaccard(G, u, v):
...     unbrs = set(G[u])
...     vnbrs = set(G[v])
...     return float(len(unbrs & vnbrs)) / len(unbrs | vnbrs)
...
>>> def my_weight(G, u, v, weight="weight"):
...     w = 0
...     for nbr in set(G[u]) & set(G[v]):
...         w += G[u][nbr].get(weight, 1) + G[v][nbr].get(weight, 1)
...     return w
...
>>> # A complete bipartite graph with 4 nodes and 4 edges
>>> B = nx.complete_bipartite_graph(2, 2)
>>> # Add some arbitrary weight to the edges
>>> for i, (u, v) in enumerate(B.edges()):
...     B.edges[u, v]["weight"] = i + 1
...
>>> for edge in B.edges(data=True):
...     print(edge)
...
(0, 2, {'weight': 1})
(0, 3, {'weight': 2})
(1, 2, {'weight': 3})
(1, 3, {'weight': 4})
>>> # By default, the weight is the number of shared neighbors
>>> G = bipartite.generic_weighted_projected_graph(B, [0, 1])
>>> print(list(G.edges(data=True)))
[(0, 1, {'weight': 2})]
>>> # To specify a custom weight function use the weight_function parameter
>>> G = bipartite.generic_weighted_projected_graph(
...     B, [0, 1], weight_function=jaccard
... )
>>> print(list(G.edges(data=True)))
[(0, 1, {'weight': 1.0})]
>>> G = bipartite.generic_weighted_projected_graph(
...     B, [0, 1], weight_function=my_weight
... )
>>> print(list(G.edges(data=True)))
[(0, 1, {'weight': 10})]

Notes

No attempt is made to verify that the input graph B is bipartite. The graph and node properties are (shallow) copied to the projected graph.

See bipartite documentation for further details on how bipartite graphs are handled in NetworkX.